| Summary: | In this paper, an extension of the generalized extreme value (GEV) distribution called the Topp Leone-GEV (TL-GEV)
distribution is applied. The TL-GEV distribution has four parameters (λ, μ, σ, ξ), and it has the three named sub-models TLGumbel (for ξ = 0), TL-Fréchet (for ξ > 0), and TL-reversed Weibull (for ξ < 0). Its properties and maximum likelihood
estimation are discussed. A data set was used to demonstrate the efficiency of the proposed distribution. The TL-GEV
distribution was employed for fitting the data and compared to some selected distributions. The two datasets represented PM2.5
data for Chiang Mai Province (Tambon Sri Phum and Tambon Chang Phueak), in Thailand. According to the KolmogorovSmirnov test, Akaike Information Criterion, and Bayesian Information Criterion, the TL-GEV distribution for ξ > 0 or TLFréchet distribution can be considered competitive. The TL-GEV distribution is an alternative flexible way to analyze any
extreme values and to estimate the return level, because the additional parameter λ provides flexibility to the distribution
affecting its skewness and kurtosis.
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